Indeed, this seems unusual in programmer land. As evidence we have a thread like the current one reaching the front page several times a day.
But your way is also my way. I am active in a very wide array of topics, and happy to flit between them. Sometimes I dive deep, but it's usually in a critical moment of synthesis when ideas developed over months or years come to clarity and I put them to action. This is working extremely well for me. I lack nothing and am at the absolute cutting edge in every topic I'm pursuing. Of course this is my opinion but it's sufficient to say that I'm happy.
It is sad to see how many people are made uncomfortable by interruption. It's the stuff of life, social life at least, and exactly what makes being human in a dense society so wonderful. I feel it represents a fundamental discomfort with being in situations out of one's control. But, that's the core of life. And for me it's where all the creative energy comes from.
edit: Reflecting on John Carmack and his big monitor. I habitually work in single window terminals with relatively low row counts and big fonts. I seem to be unable to get a benefit from seeing more stuff all at once.
edit2: And in terms of getting into flow state, for me it is always basically instantaneous. The flow is just sitting there under a few seconds of pause. Of course sitting at a computer or phone will cause wandering distraction at times, but if work is in play I can start driving at full speed in what would typically be seen as a horrifically uncomfortable position. Imagine a long distance train with two children jumping on you... If I can see my laptop and the kids at the same time, I'm flowing. I think this might be neurological somehow, due to training or genetics. It's unclear.